IJPAM: Volume 83, No. 3 (2013)

Abstract. The B-differentiability of f is defined in general vector normed
spaces, which is defined in finite dimensional Euclidean space (see [2]). Meanwhile, Gäteaux differentiability, Hadamard differentiability and Fréchet differentiability are also considered. In addition, srong Fréchet differentiability and strong Bouligand differentiability are also introduced. We present the relationships along these kinds of differentiable maps and give two examples to explain these relationships.